Enigma 136: Twelve-point square
15 October 2013
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From New Scientist #1280, 19th November 1981 [link]
“Take a large sheet of ordinary graph-paper,” said Professor Mortis, “and draw a circle with centre at any point you like. Now mark with a tiny blob any place where the circle exactly cuts one of the juncs of the graph-paper. … What? … A junc is where a north-south line cuts an east-west line, of course. … Right. … Then cut out any square you like from the graph paper. … Yes, the square can be of any size and orientation you choose… Next, count the blobs on the square. … Yes, a blob on the edge counts as on the square. … If there are fewer than 12 blobs, start again. But if there are 12 or more blobs, work out the area of the square.”
If the graph-paper is ruled at 1cm intervals, what is the smallest area I can end up with?